Jazz...
...has the diagnosis correct. It's called botrytis.
We've had a ton of rain of late which, as Jazz said, is the 'why'? part of the equation. As to what to do, I wouldn't do anything because petunias are very durable and the botrytis will cease being a problem as the rain lessens.
If you are the type who leaves no stone unturned, then, by all means, get you some fungicide on there. Be diligent in reading the label and aware of the conditions; it won't do any good to apply some protection only to have it wash off in a storm and hour or two later (which is another reason Iwouldn't bother with it). Point being there should be directions as to how long the product needs without rain.
As I write this, perhaps would you could do is just pluck all the open blooms off, assuming we're not talking about a bed of petunias with 100's of flowers. By removing them, you are removing much of the active botrytis and this will buy a little time until this wet spell passes. You'll have more color by in days.
Botrytis just exists. It is conditions, warm, wet and cool all mixing together, that spark it becoming active.